State estimation for linear impulsive differential systems through polyhedral techniques

Pages: 466 - 475, Issue Special, September 2009

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Elena K. Kostousova - Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16, S.Kovalevskaja Street, Ekaterinburg GSP-384, 620219, Russian Federation (email)

Abstract: The paper is devoted to the state estimation problem in control theory under uncertainty. The approach for estimating the reachable sets of the linear impulsive differential systems is presented. The reachable sets are approximated by the ones for special discrete time systems. The degree of convergence is established. The families of external and internal polyhedral (parallelepiped-valued and parallelotope-valued) estimates of the reachable sets of the auxiliary systems are introduced. Evolution of estimates is determined by systems of recurrence relations. The families which ensure the exact representations of the reachable sets of the auxiliary systems as well as the families of the touching and tight estimates are found. This technique gives the possibility to construct the guaranteed estimates (including $\epsilon$-touching and $\epsilon$-tight ones) for the reachable sets of the primary systems. The results of numerical simulations are presented.

Keywords:  Dynamical systems, impulsive differential systems, reachable sets, set-valued state estimation, approximation, polyhedral estimates, parallelepipeds, parallelotopes
Mathematics Subject Classification:  Primary: 93B03, 93C05, 93C15; Secondary: 52B12, 93C55

Received: July 2008;      Revised: April 2009;      Published: September 2009.